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Homework Help: Conducting Concentric Sphere

  1. Sep 23, 2007 #1
    1. The problem statement, all variables and given/known data

    A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has not net chare. a) Derive expressions for the electric field magnitude in terms of the distance r from the center for the regions r<a, a<r<b, b<r<c, r>c.

    2. Relevant equations

    E = [1/(4*pi*epsilon_0)](q/r^2)

    3. The attempt at a solution

    I've managed to correctly answer the first two parts of the problem, however when it comes to b<r<c and r>c, I do not get the answers I should.
    Apparently, for b<r<c, E = 0 since a -q cancels the inner +q. Then, for r>c, E = [1/(4*pi*epsilon_0)](q/r^2) since the total charge enclosed is +q again.

    I think my problem lies in the fact that I don't fully comprehend what a concentric sphere is or how charge distribution on a concentric sphere works. Based on the solution, I feel I should intrepret that the neutral concentric sphere is neutral because it contain an equal number of positive and negative charges that have all collected on opposite surfaces - the negative charges on the inner surface of the concentric sphere (radius b) and the positive charges on its outer surface (radius c.) Otherwise, I don't quite understand how the -q and overall +q come into play...

    Thank you very much for taking the time to read this!
    Last edited: Sep 23, 2007
  2. jcsd
  3. Sep 24, 2007 #2


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    Staff Emeritus
    Science Advisor

    This might help - http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html

    The inner sphere has charge +q. Being a conductor, the charge resides at the surface.

    It would have a surface charge density of +q/4[itex]\pi[/itex] a2.

    This positive charge induces a corresponding -q charge on the inner surface of the hollow conductor (r=b), and consequently there is a +q charge on the outer surface r = c.

    The electric flux is based on the enclosed charge, and the +q at r=a cancels the -q charge at r=b.

    Then there is a charge +q at r=c.

    The surface density of the charge at r = b is -q / 4[itex]\pi[/itex] b2, and the surface charge density at r=c is +q / 4[itex]\pi[/itex] c2.
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